Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

A lower bound for rank 2 lattice rules


Author: Friedrich Pillichshammer
Journal: Math. Comp. 73 (2004), 853-860
MSC (2000): Primary 11K06, 65D32, 41A55
DOI: https://doi.org/10.1090/S0025-5718-03-01596-5
Published electronically: July 29, 2003
MathSciNet review: 2031410
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give a lower bound for a quality measure of rank 2 lattice rules which shows that an existence result of Niederreiter is essentially best possible.


References [Enhancements On Off] (What's this?)

  • 1. Hlawka, E.: Zur angenäherten Berechnung mehrfacher Integrale. Monatsh. Math. 66: 140-151, 1962. MR 26:888
  • 2. Korobov, N.M.: Numbertheoretical Methods in Approximate Analysis. Moscow: Fizmatgiz. 1963. (In Russian.) MR 28:716
  • 3. Kuipers, L., Niederreiter, H.: Uniform Distribution of Sequences. John Wiley, New York, 1974. MR 54:7415
  • 4. Larcher, G.: A Best Lower Bound for Good Lattice Points. Monatsh. Math. 104: 45-51, 1987. MR 89f:11103
  • 5. Niederreiter, H.: Existence of Good Lattice Points in the Sense of Hlawka. Monatsh. Math. 86: 203-219, 1978. MR 80e:10039
  • 6. Niederreiter, H.: The Existence of Efficient Lattice Rules for Multidimensional Numerical Integration. Math. Comp. 58: 305-314 and S7-S16, 1992. MR 92e:65023
  • 7. Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods. No. 63 in CBMS-NSF Series in Applied Mathematics. SIAM, Philadelphia, 1992. MR 93h:65008
  • 8. Niederreiter, H., Sloan, I.H.: Lattice rules for multiple integration and discrepancy. Math. Comp. 54: 303-312, 1990. MR 90f:65036
  • 9. Sloan, I.H., Joe, S.: Lattice Methods for Multiple Integration. Oxford Univ. Press, New York and Oxford, 1994. MR 98a:65026
  • 10. Sloan, I.H., Lyness, J.N.: Lattice rules: Projection regularity and unique representations. Math. Comp. 54: 649-660, 1990. MR 91a:65062

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11K06, 65D32, 41A55

Retrieve articles in all journals with MSC (2000): 11K06, 65D32, 41A55


Additional Information

Friedrich Pillichshammer
Affiliation: Institut für Analysis, Universität Linz, Altenbergerstraße 69, A-4040 Linz, Austria
Email: friedrich.pillichshammer@jku.at

DOI: https://doi.org/10.1090/S0025-5718-03-01596-5
Keywords: Rank 2 lattice rule, quadrature error bound
Received by editor(s): August 5, 2002
Received by editor(s) in revised form: November 8, 2002
Published electronically: July 29, 2003
Additional Notes: Supported by the Austrian Research Foundation (FWF), project S 8305.
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society